Sequential Designs with Application in Software Engineering

Title from PDF of title page, viewed on March 31, 2014Dissertation advisor: Kamel RakabVitaIncludes bibliographical references (pages 77-81)Thesis (Ph. D.)--Dept. of Mathematics and Statistics and Dept. of Computer Science and Electrical Engineering. University of Missouri, Kansas City, 2013Presented here is a Bayesian approach to test case allocation in the software reliability estimation. Bayesian analysis allows us to update our beliefs about the reliability of a particular partition as we test, and thus, dynamically re refine our allocation of test cases during the reliability testing process. We started with a fully sequential sampling scheme to estimate the reliability of a software system using partition testing. We have shown both theoretically and through simulation that the proposed scheme always performs at least as well as fixed sampling approaches where test case allocation is predetermined, and in all but the most unlikely circumstances, outperform them. Based on the sequential allocation, a multistage sampling scheme is established, which is less time consuming and more e efficient. Meanwhile, an e efficient sampling scheme is also developed to accommodate more situations. In the last chapter, we extend our study from parallel systems to series systems. We again use a Bayesian approach to allocate test cases to estimate the reliability of a series system with two components. A second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound.Abstract -- List of tables -- List of notations -- Acknowledgement -- Introduction -- A fully sequential test allocation for software reliability estimation -- A multistage sequential test allocation for software reliability estimation -- An efficient test allocation for software reliability estimation -- Test allocation for estimating reliability of series systems with two components -- Summary and conclusion -- Appendix -- Tables -- Referenc

Efficient sequential designs with asymptotic second-order lower bound of Bayes risk for estimating product of means

Title from PDF of title page viewed January 8, 2020Dissertation advisor: Kamel Rekab and Deep Medhi,VitaIncludes bibliographical references (page 60-62)Thesis (Ph.D.)--Department of Mathematics and Statistics, School of Computing and Engineering. University of Missouri--Kansas City, 2019In order to estimate the reliability of sequentially designed procedures under the Bayesian framework with conjugate priors, a sharp lower bound for the Bayes risk has been derived. Chapter 1 and 2 introduce the background and fundamental concepts and theorems of this study. Chapter 3 focuses on deriving second-order efficiency of Bayes risk for two independent components in the one-parameter exponential family which includes the most common distribution in application of reliability testing, Bernoulli distribution. Chapter 3 also uses Monte Carlo simulations with several proposed sequential designs to illustrate optimality of the second-order efficiency. Then Chapter 4 extends the result to k (k>2) independent components sequentially designed systems. The same Monte Carlo simulations were performed to assure that the second order lower bound is achieved.Introduction -- Conceptual framework -- Second-order efficiency for estimating product of 2 components in exponential family -- Second-order efficiency for estimating product of K components -- Conclusio